My toro rider with a 9 hp briggs had a similar problem with consumption. It's about 18 years old, and my grandfather bought it new. He then passed it on to my dad, then he passed it on to me.
I changed out the oil to Pennzoil 5w30 dino, and about 5 hours of run time after, I had to add 12oz of oil.
I got it from my dad, and I believe the last fill it had was Valvoline WB 5w30 off the tap at his dealership.
That seemed to last longer, though I don't know why.
They are both the same viscosity, and from what I've seen in voa's, Pennzoil has a better ad pack.
I don't get it. I topped off with some generic Amalie (parts plus branded) 10w40.
I think I'm going to Rotella, or Delo 15w40 next oil change.